Molecular hydrogen and its isotopic and ionic species are benchmark systems for testing quantum chemical theory. Advances in molecular energy structure calculations enable the experimental verification of quantum electrodynamics and potentially a determination of the proton charge radius from H_{2} spectroscopy. We measure the ground state energy in ortho-H_{2} relative to the first electronically excited state by Ramsey-comb laser spectroscopy on the EF^{1}Σ_{g}^{+}-X^{1}Σ_{g}^{+}(0,0) Q1 transition. The resulting transition frequency of 2 971 234 992 965(73) kHz is 2 orders of magnitude more accurate than previous measurements. This paves the way for a considerably improved determination of the dissociation energy (D_{0}) for fundamental tests with molecular hydrogen.

High-precision spectroscopy in systems such as molecular hydrogen and helium ions is very interesting in view of tests of quantum electrodynamics and the proton radius puzzle. However, the required deep ultraviolet and shorter wavelengths pose serious experimental challenges. Here we show Ramsey-comb spectroscopy in the deep ultraviolet for the first time, thereby demonstrating its enabling capabilities for precision spectroscopy at short wavelengths. We excite ^{84}Kr in an atomic beam on the two-photon 4p^{6}→4p^{5}5p[1/2]_{0} transition at 212.55 nm. It is shown that the ac-Stark shift is effectively eliminated, and combined with a counterpropagating excitation geometry to suppress Doppler effects, a transition frequency of 2 820 833 101 679(103) kHz is found. The uncertainty of our measurement is 34 times smaller than the best previous measurement, and only limited by the 27 ns lifetime of the excited state.

High-harmonic generation (HHG) is widely used for up-conversion of amplified (near) infrared ultrafast laser pulses to short wavelengths. We demonstrate that Ramsey-comb spectroscopy, based on two such pulses derived from a frequency-comb laser, enables us to observe phase effects in this process with a few mrad precision. As a result, we could perform the most accurate spectroscopic measurement based on light from HHG, illustrated with a determination of the 5p 6 → 5p 5 8s 2 [3/2]1 transition at 110 nm in 132 Xe. We improve its relative accuracy 10 4 times to a value of 2.3 × 10 −10 . This is 3.6 times better than shown before involving HHG, and promising to enable 1S − 2S spectroscopy of He + for fundamental tests.High-precision spectroscopy in calculable atomic and molecular systems is at the heart of the most precise tests of bound-state quantum electrodynamics (QED) and searches for new physics beyond the Standard Model [1][2][3][4][5][6]. Instrumental in this development was the invention of the optical frequency comb (FC) [7,8] which enables precise optical frequency measurements referenced to an atomic clock. However, uncertainties in finite nuclearsize effects are hampering further progress [9]. Instead, spectroscopy has been used to measure the proton size in atomic and muonic hydrogen, but with partly conflicting results [10][11][12][13][14][15][16]. High-precision spectroscopy of the 1S − 2S transition in He + would provide new possibilities for fundamental tests as the uncertainty there is less dominated by nuclear size effects [17]. Combined with muonic He + spectroscopy [18,19] one can extract e.g. the alpha particle radius or the Rydberg constant. A major experimental challenge arises from the requirement of extreme ultraviolet (XUV) light at 60 nm (or shorter), to excite the transition. A similar challenge exist for spectroscopy of highly-charged ions [5], or the Thorium nuclear clock transition near 150 nm in the vacuum ultraviolet (VUV) [20,21]. At those wavelengths a relative accuracy of 0.1 ppm has been achieved with Fouriertransform spectroscopy techniques [22], and 0.03 ppm with low harmonics from nanosecond pulsed lasers [23]. A higher accuracy can be reached with light from highharmonic generation (HHG), induced by focusing ultrafast high-energy laser pulses in a noble gas at intensities of ∼ 10 14 W/cm 2 . The process can be understood using the three-step model [24,25], involving tunnel-ionization and recollision of an electron. This highly coherent process leads to the generation of a series of odd harmonics, which are tightly linked to the fundamental wave [26][27][28][29][30]. In combination with frequency-comb lasers, it has been used to achieve a spectroscopic accuracy of about 1 ppb at VUV and XUV wavelengths [31,32]. To improve on this we recently developed the Ramseycomb spectroscopy (RCS) method [33,34], based on pairs of powerful amplified FC pulses in a Ramsey-type [35] excitation scheme. Using only two pulses can compro-mise the accuracy provided by the FC laser [31], but th...

High-precision laser spectroscopy of atomic hydrogen has led to an impressive accuracy in tests of bound-state quantum electrodynamics (QED). At the current level of accuracy many systematics have to be studied very carefully and only independent measurements provide the ultimate cross-check. This has been proven recently by measurements in muonic hydrogen, eventually leading to a significant shift of the CODATA recommended values of the proton charge radius and the Rydberg constant. We aim to contribute to tests of fundamental physics by measuring the 1S-2S transition in the He + ion for the first time. Combined with measurements in muonic helium ions this can probe the value of the Rydberg constant, test higher-order QED terms, or set benchmarks for ab initio nuclear polarizability calculations. We extend the Ramsey-comb spectroscopy method to the XUV using high-harmonic generation in order to excite a single, trapped He + ion.

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In attempts to unify the four known fundamental forces in a single quantum-consistent theory, it is suggested that Lorentz symmetry may be broken at the Planck scale. Here we search for Lorentz violation at the low-energy limit by comparing orthogonally oriented atomic orbitals in a Michelson-Morley-type experiment. We apply a robust radiofrequency composite pulse sequence in the 2F7/2 manifold of an Yb+ ion, extending the coherence time from 200 μs to more than 1 s. In this manner, we fully exploit the high intrinsic susceptibility of the 2F7/2 state and take advantage of its exceptionally long lifetime. We match the stability of the previous best Lorentz symmetry test nearly an order of magnitude faster and improve the constraints on the symmetry breaking coefficients to the 10−21 level. These results represent the most stringent test of this type of Lorentz violation. The demonstrated method can be further extended to ion Coulomb crystals.

and bound-state QED tests based on precision spectroscopy in atoms, molecules and highly charged ions (see, e.g., [5][6][7][8][9][10]). Moreover, in the pursuit of testing QED ever better, substantial efforts have been made to extract fundamental quantities such as the Rydberg constant R ∞ and the proton charge radius. Both can be obtained from spectroscopy of atomic hydrogen, assuming that QED is sufficiently precise. However, when the CREMA collaboration determined the proton charge radius from spectroscopy in muonic hydrogen (consisting of a proton and a muon), it leads to a considerable (7σ) mismatch with the value extracted from normal (electronic) hydrogen [11][12][13]. This mismatch, known as the proton radius puzzle, remains to be explained and requires more spectroscopic measurements, e.g., in systems other than (muonic) hydrogen. Recent results on muonic deuterium [14] reveal that also the deuteron radius is significantly smaller (7.5 σ) than the radius based on normal deuterium spectroscopy.Interesting candidates for precision spectroscopy to solve this puzzle need to be sufficiently simple for precise theoretical treatment. One example is molecular hydrogen, made possible by recent improvements in theory [15]. Another is He + [16], which can be compared to muonic-He + spectroscopy [13]. The experimental challenge is the short wavelengths required for excitation, which ranges from the deep UV (≈ 200 nm) for H 2 to extreme ultraviolet (XUV, < 60 nm) for He + .Such short wavelengths are typically obtained by frequency upconversion of near-infrared lasers in nonlinear crystals or noble gases. One can use a frequency-comb (FC) laser as the fundamental laser and take advantage of its excellent spectral resolution and pulse peak power, to perform direct frequency-comb spectroscopy (DFCS) [17][18][19]. To achieve sufficient upconversion to the UV or XUV range, several approaches have been investigated. AbstractIn this paper, we present a detailed account of the first precision Ramsey-comb spectroscopy in the deep UV. We excite krypton in an atomic beam using pairs of frequency-comb laser pulses that have been amplified to the millijoule level and upconverted through frequency doubling in BBO crystals. The resulting phase-coherent deep-UV pulses at 212.55 nm are used in the Ramseycomb method to excite the two-photon 4p 6 → 4p 5 5p[1/2] 0 transition. For the 84 Kr isotope, we find a transition frequency of 2829833101679(103) kHz. The fractional accuracy of 3.7 × 10 −11 is 34 times better than previous measurements, and also the isotope shifts are measured with improved accuracy. This demonstration shows the potential of Ramsey-comb excitation for precision spectroscopy at short wavelengths.

We study heating of motional modes of a single ion and of extended ion crystals trapped in a linear radio frequency (rf) Paul trap with a precision of Δ n ̄ ̇ ≈ 0.1 phonons s−1. Single-ion axial and radial heating rates are consistent and electric field noise has been stable over the course of four years. At a secular frequency of ω sec = 2π × 620 kHz, we measure n ̄ ̇ = 0.56 ( 6 ) phonons s−1 per ion for the center-of-mass (com) mode of linear chains of up to 11 ions and observe no significant heating of the out-of-phase (oop) modes. By displacing the ions away from the nodal line, inducing excess micromotion, rf noise heats the com mode quadratically as a function of radial displacement r by n ̄ ̇ ( r ) / r 2 = 0.89 ( 4 ) phonons s−1 μm−2 per ion, while the oop modes are protected from rf-noise induced heating in linear chains. By changing the quality factor of the resonant rf circuit from Q = 542 to Q = 204, we observe an increase of rf noise by a factor of up to 3. We show that the rf-noise induced heating of motional modes of extended crystals also depends on the symmetry of the crystal and of the mode itself. As an example, we consider several 2D and 3D crystal configurations. Heating rates of up to 500 ph s−1 are observed for individual modes, giving rise to a total kinetic energy increase and thus a fractional time dilation shift of up to −0.3 × 10−18 s−1 of the total system. In addition, we detail how the excitation probability of the individual ions is reduced and decoherence is increased due to the Debye–Waller effect.